I was looking at the hands from the recent 2013 World Computer Bridge Championship (held in Bali along with all the human events). I was very surprised to find that one of the programs in the finals of the championships misplayed the following hand.

West

♠

QJ98

♥

4

♦

AK6

♣

AQJ72

North

♠

107632

♥

10

♦

7432

♣

1054

East

♠

A5

♥

AKJ76532

♦

J9

♣

K

South

♠

K4

♥

Q98

♦

Q1085

♣

9863

W

N

E

S

P

1♣

P

2♥

P

2♠

P

3♥

P

4N

P

5♣

P

6N

P

P

P

D

6NT West

NS: 0 EW: 0

North led a diamond, and the hand is straightforward - set up the hearts with a finesse, losing a trick if necessary. Unless hearts are 4-0 offside, you make.

Instead, declarer led the ♠Q for a finesse at trick 2. When it lost and a diamond was returned, the heart finesse was still a legitimate chance to make the contract, if it were on. But the computer just cashed out top winners for down 3.

This surprises me because declarer play would seem to be the most tractable part of writing a computer bridge program (no partnership agreements involved), and I would have thought a hand like this which is nothing but counting tricks and a simple suit combination would be solved correctly by modern programs. Whether you use some kind of planning algorithm or a Monte Carlo simulation, you should get the right answer. If a top program in the world championships cannot play a hand like this correctly (and it isn't some sort of unexpected bug that could be lurking in any program, of course), then computer bridge has a much longer way to go than I thought.

Update: I entered the hand into the Bridge Calculator by Piotr Beling which includes a single dummy solver which does a simple Monte Carlo simulation. After around 1000 samples, it is clear that leading a heart at trick 2 is about 5% better than leading the ♠Q. (More samples do not change the result.) Curiously, though, the simulator seems to prefer leading a club at trick 2 by a tiny margin over a heart. But as soon as the club trick is played (with both defenders following), the probability of making drops about 3%, which is strange since the club trick will almost always be played with both following and thus contributes no information.

(Note: All percentage changes reported above are absolute, not relative: A change from 90% to 95% is 5% better.)

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